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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Integration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral. See Examples 1, 2, 3, and 4.

x e 6 x   d x

To determine

To calculate: The value of indefinite integral xe6xdx.

Explanation

Given Information:

The provided indefinite integral is xe6xdx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

eaxdx=eaxa+C

Calculation:

Consider the indefinite integral xe6xdx

Here,

dv=e6xdx and u=x

First find v,

dv=e6xdxdv=e6xdx

On further solving,

v=e6x6 …… (1)

Find du:

u=x

Differentiate both side with respect x;

dudx=dxdxdudx=1

And,

du=1dx …… (2)

Apply integration by parts formula and substitute equation (1) and (2) in udv=uvvdu,

xe6x=x(e6x6)e6x61dx

Apply the formula eaxdx=eaxa+C,

x

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